Page 131 - Chemical equilibria Volume 4

Determination of the Values Associated with Reactions – Equilibrium Calculations 107
The entropy of the reaction varies with temperature in accordance with
relation [4.6], as a function of the specific heat capacity at constant
pressure and of the temperature:
⎛ ∂ Δ S Δ C P
r ⎞
r
⎜ ⎟ = [4.6]
⎝ ∂ T P ⎠ T
If we consider a substance undergoing an allotropic transformation in the
solid state at temperature T a, which melts at temperature T F and boils at
temperature T Eb, to integrate expressions [4.4] and [4.6], it is necessary to
divide the temperature interval between the initial temperature T 0 and the
temperature T into slices. Each slice is characterized by a phase and
therefore a function of the molar specific heat capacity at constant pressure
with changing temperature. Thus, integration of equation [4.4] involves two
types of terms:
2 T
1) integral terms in the form ∫ ΔC P (φ) dT in the domain of stability of
1 T
phase ϕ;

2) terms due to the changes which stem from the enthalpies associated
with the phase changes of the components in the reaction. For the phase
change Δφ of component A k, whose algebraic stoichiometric number in the
reaction is ν k, the corresponding term is: Δ Hν k Δφ k .

Thus, the enthalpy takes the form of a sum similar to equation [4.7], in
which the number of terms depends on the initial temperature T 0 at which we
know the enthalpy, and on the number of state changes of the substance
between the temperature T 0 and the effective temperature T.

T
ν
Δ H T = Δ H 0 + ∑ ∫ Δ C P ) φ ( dT + ∑ k Δ H k [4.7]
r
Δφ
r
r
φ T Δφ, k
Δφ
We proceed in the same way for the integration of the entropy function
on the basis of relation [4.6], with the same division of the temperature
2 T Δ C (φ)
range. We find integral terms in the form ∫ r P dT and terms of state
1 T T